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Levalbuterol (Jaworowicz 2006)

Source: vignettes/articles/Jaworowicz_2006_levalbuterol.Rmd
Jaworowicz_2006_levalbuterol.Rmd
library(nlmixr2lib)
library(PKNCA)
#> 
#> Attaching package: 'PKNCA'
#> The following object is masked from 'package:stats':
#> 
#>     filter
library(rxode2)
#> rxode2 5.1.2 using 2 threads (see ?getRxThreads)
#>   no cache: create with `rxCreateCache()`
library(dplyr)
#> 
#> Attaching package: 'dplyr'
#> The following objects are masked from 'package:stats':
#> 
#>     filter, lag
#> The following objects are masked from 'package:base':
#> 
#>     intersect, setdiff, setequal, union
library(tidyr)
library(ggplot2)

Model and source

  • Citation: Jaworowicz D, Maier G, Baumgartner RA, Hsu R, Grasela TH. Population pharmacokinetics of (R)-albuterol following inhaled levalbuterol or racemic albuterol via a hydrofluoroalkane metered dose inhaler in pediatric and adult asthma patients. Poster T3350, American Association of Pharmaceutical Scientists Annual Meeting and Exposition, San Antonio, TX, October 29 - November 2, 2006. Sepracor, Inc. / Cognigen Corporation.
  • Description: Two-compartment population PK model for (R)-albuterol following inhaled levalbuterol (90 ug) or racemic albuterol (180 ug) via a hydrofluoroalkane metered-dose inhaler in pediatric (4-11 years) and adult (12-81 years) asthma patients. First-order absorption, linear elimination, body-weight effects on apparent clearance (linear-additive) and central volume (power), and a pediatric-vs-adult split on absorption rate. The reference parameters are the Adult / Study 051-353 / single-dose levalbuterol-visit values (bioavailability anchor F1 = 1).
  • Article: AAPS 2006 Annual Meeting Poster T3350 (no DOI; conference abstract / poster)

Population

The source poster pooled 632 subjects (81 pediatric, ages 4-11 years; 551 adult, ages 12-81 years) from three randomized, multi-center, placebo- and active-controlled, double-blind, parallel-design Phase 3 trials in adult and pediatric asthma patients (Sepracor studies 051-353, 051-355, and a third pediatric trial). 429 subjects received 90 ug levalbuterol QID via HFA MDI and 203 received 180 ug racemic albuterol QID. PK was measured as (R)-albuterol plasma concentration (n = 3791 samples) after the first dose and after 4 weeks (pediatric) or 8 weeks (adult) of QID dosing. Adult mean (SD) weight was 80.8 (22.3) kg; pediatric mean was 37.1 (15.2) kg. Cohort-pooled median weight 75.2 kg; the model uses 74.8 kg as the WT covariate reference (Equations 1-2 of the poster).

The same information is available programmatically via the model’s population metadata (readModelDb("Jaworowicz_2006_levalbuterol")$population).

Source trace

The per-parameter origin is recorded as an in-file comment next to each ini() entry in inst/modeldb/specificDrugs/Jaworowicz_2006_levalbuterol.R. The table below collects them in one place for review.

Equation / parameter Value Source location
Structural model: 2-compartment, first-order absorption, linear elimination n/a Results section “Final PPK Model”
lka (Adult Ka) log(6.28) Table 2 row 1 (6.28 1/hr, %SEM 7.8)
e_child_ka (CHILD effect) log(3.08 / 6.28) Table 2 row 2 (Ka pediatric 3.08 1/hr)
lcl (CL intercept) log(59.1) Table 2 row “CL/F” (59.1 L/hr) + Equation 1
e_wt_cl (WT slope on CL) 0.477 Table 2 row “Slope Term for Body Weight on CL/F” + Equation 1
lvc (Vc reference) log(527) Table 2 row “Vc/F” (527 L) + Equation 2
e_wt_vc (WT exponent on Vc) 0.361 Table 2 row “Power Term for Body Weight on Vc/F” + Equation 2
lvp (Vp) log(506) Table 2 row “Vp” (506 L)
lq (Q) log(100) Table 2 row “Q” (100 L/hr)
lfdepot (F1 reference) fixed log(1) Table 2 footnote b (F1 = 1 for Adult Study 051-353 single-dose levalbuterol visit)
etalka (Adult Ka IIV) 0.3764 Table 2 (67.60 %CV); omega^2 = log(1 + 0.676^2)
etalcl 0.1450 Table 2 (39.50 %CV); omega^2 = log(1 + 0.395^2)
etalvc 0.2078 Table 2 (48.06 %CV); omega^2 = log(1 + 0.4806^2)
etalvp 0.3927 Table 2 (69.35 %CV); omega^2 = log(1 + 0.6935^2)
etalfdepot 0.0574 Table 2 (Adult Study 051-355 LEV F1 IIV 24.31 %CV); omega^2 = log(1 + 0.2431^2)
propSd 0.2133 Table 2 footnote d (proportional component from %CV(IPRED = 900 pg/mL) = 21.33 %)
addSd 0.00134 ng/mL Table 2 footnote d (additive component derived from %CV(25 pg/mL) - %CV(900 pg/mL) spread; 1.34 pg/mL = 1.34e-3 ng/mL)
Equation 1: TVCL = 59.1 + 0.477 * (WT - 74.8) n/a Equation 1
Equation 2: TVVc = 527 * (WT / 74.8)^0.361 n/a Equation 2

Virtual cohort

The original observed data are not publicly available. The validation below simulates two virtual cohorts whose body-weight distributions approximate the pooled adult and pediatric demographics reported in Table 1 of the poster:

  • Adult cohort (n = 50): WT ~ Normal(mean = 80.8 kg, SD = 22.3 kg), CHILD = 0.
  • Pediatric cohort (n = 50): WT ~ Normal(mean = 37.1 kg, SD = 15.2 kg), CHILD = 1.

Levalbuterol is dosed at 90 ug QID (every 6 hours) for 7 days; the dense post-dose sampling (0.25, 0.5, 1, 2, 4, 6, 8 hours after the final dose) matches the second-visit sampling schedule used in the trials.

Cohort-specific bioavailability. The model anchors f(depot) at F1 = 1 because the source poster uses the Adult / Study 051-353 / Visit 6 (single-dose levalbuterol) cohort as the bioavailability reference (Table 2 footnote b). The steady-state visits reported in Table 3, however, used the estimated relative F1 values: 0.715 (mean of the Adult / Study 051-353 and Adult / Study 051-355 steady-state estimates, 0.725 and 0.707) for the adult-LEV cohort and 0.550 for the pediatric-LEV cohort. To reproduce Table 3, the dose amount delivered to each subject is scaled by the cohort-specific relative F1 (the model’s F1 defaults to 1, so scaling the dose amount is operationally equivalent to applying a per-cohort F1).

set.seed(20061102) # AAPS 2006 closing date

n_per_group <- 50L
qid_interval <- 6 # hours (QID = every 6 hours)
n_doses_qid  <- 7 * 4 # 7 days x 4 doses/day = 28 doses
nominal_dose <- 90 # ug levalbuterol per actuation

# Cohort-specific relative bioavailability for the steady-state visits.
# Table 2: Adult LEV F1 0.725 (Study 051-353) and 0.707 (Study 051-355) ->
# mean 0.716; Pediatric LEV F1 0.550.
f1_adult_lev <- mean(c(0.725, 0.707)) # = 0.716
f1_ped_lev   <- 0.550

dose_times <- seq(0, by = qid_interval, length.out = n_doses_qid)
last_dose  <- dose_times[n_doses_qid]
obs_times  <- sort(unique(c(
  last_dose + c(0, 0.25, 0.5, 1, 2, 4, 6, 8)
)))

make_cohort <- function(n, wt_mean, wt_sd, child, treatment, dose_amount,
                        id_offset = 0L) {
  ids <- id_offset + seq_len(n)
  # Truncate WT to a physiologically plausible range to avoid extreme draws
  # from the Normal that would distort the WT covariate scaling.
  wt_range <- if (child == 1L) c(14.5, 89.4) else c(35.8, 167.5)
  WT_i <- pmin(pmax(rnorm(n, wt_mean, wt_sd), wt_range[1]), wt_range[2])

  per_subj <- tibble::tibble(
    id        = ids,
    WT        = WT_i,
    CHILD     = child,
    treatment = treatment
  )

  doses <- per_subj |>
    tidyr::expand_grid(time = dose_times) |>
    dplyr::mutate(
      amt  = dose_amount,
      evid = 1L,
      cmt  = "depot"
    )

  obs <- per_subj |>
    tidyr::expand_grid(time = obs_times) |>
    dplyr::mutate(
      amt  = 0,
      evid = 0L,
      cmt  = "central"
    )

  dplyr::bind_rows(doses, obs) |>
    dplyr::arrange(id, time, dplyr::desc(evid))
}

events <- dplyr::bind_rows(
  make_cohort(n_per_group, wt_mean = 80.8, wt_sd = 22.3,
              child = 0L, treatment = "Adult LEV",
              dose_amount = nominal_dose * f1_adult_lev,
              id_offset = 0L),
  make_cohort(n_per_group, wt_mean = 37.1, wt_sd = 15.2,
              child = 1L, treatment = "Pediatric LEV",
              dose_amount = nominal_dose * f1_ped_lev,
              id_offset = n_per_group)
)

stopifnot(!anyDuplicated(unique(events[, c("id", "time", "evid")])))

Simulation 

mod <- readModelDb("Jaworowicz_2006_levalbuterol")

sim <- rxode2::rxSolve(
  mod,
  events = events,
  keep   = c("WT", "CHILD", "treatment")
) |>
  as.data.frame()
#> ℹ parameter labels from comments will be replaced by 'label()'

Replicate Figure 1 - last-interval concentration-time profiles

Poster Figure 1 shows (R)-albuterol plasma concentration-time scatterplots for adults and pediatric subjects receiving either levalbuterol or racemic albuterol via HFA MDI; the curves are not numerically tabulated. The simulation below plots the median and 90 % prediction interval of Cc over the final dosing interval, converted to pg/mL to match the poster’s reporting units, by cohort (adult vs pediatric levalbuterol).

sim_last_interval <- sim |>
  dplyr::mutate(time_post_last = time - last_dose,
                Cc_pg           = Cc * 1000) |>
  dplyr::filter(time_post_last >= 0)

interval_summary <- sim_last_interval |>
  dplyr::group_by(treatment, time_post_last) |>
  dplyr::summarise(
    Q05    = quantile(Cc_pg, 0.05, na.rm = TRUE),
    Q50    = quantile(Cc_pg, 0.50, na.rm = TRUE),
    Q95    = quantile(Cc_pg, 0.95, na.rm = TRUE),
    .groups = "drop"
  )

ggplot(interval_summary, aes(x = time_post_last, y = Q50)) +
  geom_ribbon(aes(ymin = Q05, ymax = Q95, fill = treatment), alpha = 0.25) +
  geom_line(aes(colour = treatment), linewidth = 0.8) +
  scale_y_continuous() +
  labs(
    x = "Time since last QID dose (hours)",
    y = "(R)-Albuterol plasma concentration (pg/mL)",
    title = "Last-interval steady-state (R)-albuterol profile",
    caption = "Median and 90 % prediction interval. Replicates the steady-state visit shown in Figure 1 of Jaworowicz 2006."
  ) +
  theme_bw()

PKNCA validation

NCA at steady state on the last QID interval. Poster Table 3 reports Mean (SD) of Cmax (pg/mL), Tmax (hr), and AUC(0-6) (pg*hr/mL) derived from individual model-predicted PK profiles, separately for adult and pediatric levalbuterol recipients.

sim_nca <- sim |>
  dplyr::filter(!is.na(Cc)) |>
  dplyr::mutate(time_post_last = time - last_dose,
                Cc_pg           = Cc * 1000) |>
  dplyr::filter(time_post_last >= 0) |>
  dplyr::select(id, treatment, time = time_post_last, Cc = Cc_pg)

# Guarantee a time-zero row per (id, treatment); pre-dose Cc = 0 is the
# correct anchor for an extravascular dose at the start of the interval.
sim_nca <- dplyr::bind_rows(
  sim_nca,
  sim_nca |>
    dplyr::distinct(id, treatment) |>
    dplyr::mutate(time = 0, Cc = 0)
) |>
  dplyr::distinct(id, treatment, time, .keep_all = TRUE) |>
  dplyr::arrange(id, treatment, time)

conc_obj <- PKNCA::PKNCAconc(sim_nca, Cc ~ time | treatment + id)

dose_df <- events |>
  dplyr::filter(evid == 1L) |>
  dplyr::group_by(id, treatment) |>
  dplyr::summarise(amt = dplyr::first(amt), .groups = "drop") |>
  dplyr::mutate(time = 0)

dose_obj <- PKNCA::PKNCAdose(dose_df, amt ~ time | treatment + id)

intervals <- data.frame(
  start    = 0,
  end      = 6,
  cmax     = TRUE,
  tmax     = TRUE,
  auclast  = TRUE
)

nca_data    <- PKNCA::PKNCAdata(conc_obj, dose_obj, intervals = intervals)
nca_res     <- PKNCA::pk.nca(nca_data)
nca_summary <- as.data.frame(nca_res$result)

nca_wide <- nca_summary |>
  dplyr::filter(PPTESTCD %in% c("cmax", "tmax", "auclast")) |>
  dplyr::select(treatment, id, PPTESTCD, PPORRES) |>
  tidyr::pivot_wider(names_from = PPTESTCD, values_from = PPORRES)

per_treatment_summary <- nca_wide |>
  dplyr::group_by(treatment) |>
  dplyr::summarise(
    Cmax_pg_per_mL_mean    = mean(cmax,    na.rm = TRUE),
    Cmax_pg_per_mL_sd      = sd(cmax,      na.rm = TRUE),
    Tmax_hr_mean           = mean(tmax,    na.rm = TRUE),
    Tmax_hr_sd             = sd(tmax,      na.rm = TRUE),
    AUC0_6_pg_hr_per_mL_mean = mean(auclast, na.rm = TRUE),
    AUC0_6_pg_hr_per_mL_sd   = sd(auclast,   na.rm = TRUE),
    .groups = "drop"
  )

Comparison against Poster Table 3 

published <- tibble::tribble(
  ~treatment,        ~Cmax_pg_per_mL_mean, ~Cmax_pg_per_mL_sd, ~Tmax_hr_mean, ~Tmax_hr_sd, ~AUC0_6_pg_hr_per_mL_mean, ~AUC0_6_pg_hr_per_mL_sd,
  "Adult LEV",       199.61,               108.56,             0.54,          0.16,        692.41,                    414.03,
  "Pediatric LEV",   162.48,                88.49,             0.76,          0.35,        578.93,                    307.42
)

compare <- dplyr::bind_rows(
  per_treatment_summary |> dplyr::mutate(source = "Simulated (this vignette)"),
  published              |> dplyr::mutate(source = "Published (Table 3)")
) |>
  dplyr::select(source, treatment, dplyr::everything())

knitr::kable(
  compare,
  digits  = 2,
  caption = "Steady-state NCA comparison: simulated virtual cohorts vs Poster Table 3 (Jaworowicz 2006). Units: Cmax pg/mL, Tmax hr, AUC(0-6) pg*hr/mL."
)
Steady-state NCA comparison: simulated virtual cohorts vs Poster Table 3 (Jaworowicz 2006). Units: Cmax pg/mL, Tmax hr, AUC(0-6) pg*hr/mL.
source treatment Cmax_pg_per_mL_mean Cmax_pg_per_mL_sd Tmax_hr_mean Tmax_hr_sd AUC0_6_pg_hr_per_mL_mean AUC0_6_pg_hr_per_mL_sd
Simulated (this vignette) Adult LEV 251.18 105.08 0.58 0.29 1157.62 574.15
Simulated (this vignette) Pediatric LEV 276.93 114.60 0.72 0.32 1335.21 579.16
Published (Table 3) Adult LEV 199.61 108.56 0.54 0.16 692.41 414.03
Published (Table 3) Pediatric LEV 162.48 88.49 0.76 0.35 578.93 307.42

Assumptions and deviations

  • Single Ka IIV variance for both cohorts. The poster reports separate IIVs for adult (67.60 %CV) and pediatric (74.63 %CV) Ka. The model uses the adult variance for the single shared etalka; this slightly under-states pediatric Ka variability. Both are similar (omega^2 = 0.376 vs 0.442) and the effect on simulated Cmax/Tmax is small.
  • F1 anchored at the reference cohort. F1 = 1 corresponds to the Adult / Study 051-353 / single-dose levalbuterol visit (Table 2 footnote b). Other strata reported with relative F1 values (Adult LEV Study 051-355 0.707, Adult LEV Study 051-353 non-SD visits 0.725, Pediatric LEV 0.550, Adult RAC Study 051-355 1.01, Adult RAC Study 051-353 SD 0.880, Pediatric RAC 0.830) are not encoded as separate covariate effects; downstream users simulating those strata should scale f(depot) accordingly or re-fit lfdepot.
  • Interoccasion variability on F1 omitted. The poster’s Table 2 reports IOV on F1 (pediatric 46.69 %CV; Adult 051-355 35.21 %CV; Adult 051-353 LEV 32.71 %CV). This nlmixr2lib model does not encode an IOV term; the between-subject IIV on F1 (24.31 %CV) is included as etalfdepot.
  • Racemic-albuterol dosing not modelled directly. Racemic albuterol dosing (180 ug RA = 90 ug R-albuterol + 90 ug S-albuterol; only R is modelled) would require either a 50 % dose-amount scaling and a stratum-specific F1, or treating RA as a re-parameterised LEV regimen.
  • Residual error reconstruction. Table 2 lists “Additive RV (sigma2) = 0.0455” and “Ratio of Additive/Proportional RV components (sigma2/sigma1) = 35.2” in NONMEM internal-scale variance units; the realised CV is reported in footnote d as 21.99 % at IPRED = 25 pg/mL and 21.33 % at IPRED = 900 pg/mL. Solving %CV^2 = sigma_prop^2 + (sigma_add / IPRED)^2 at these two anchors gives proportional SD = 0.2133 and additive SD = 1.34 pg/mL. The raw Table 2 entries are NONMEM-scale and do not transfer directly to the SD-parameterised rxode2 propSd / addSd surface used here.
  • Virtual cohort weight distributions are normal-truncated. Body weights are drawn from Normal(mean, SD) and truncated to the cohort-specific observed weight range (Table 1: adults 35.8-167.5 kg; pediatrics 14.5-89.4 kg) to avoid implausible draws.
  • Steady state is achieved after one week of QID dosing. The clinical protocol used 4 weeks (pediatric) or 8 weeks (adult); the seven days used here are sufficient to bring the (R)-albuterol plasma concentration to steady state (terminal half-life ~14 hours from the central + peripheral disposition) and to populate the Table 3 intervals.
  • Simulated NCA exceeds Poster Table 3 by ~50-100 percent. The simulated Cavg(SS) for the adult-LEV cohort is approximately F1 * Dose / (CL/F * tau) = 0.715 * 90 / (62 * 6) = 173 pg/mL, giving AUC(0-tau) ~ 1040 pghr/mL – about 50 percent higher than the published 692 pghr/mL in Table 3. The pediatric cohort exceeds Table 3 by a larger factor (~100 percent). The structural model and parameter values in this nlmixr2lib model are faithful to the poster’s Table 2 and Equations 1-2 as published; the Table 3 NCA values appear internally inconsistent with the F1 anchor and CL/F parameters reported in Table 2 in a way that cannot be reconciled without access to the underlying analysis dataset. Possible explanations (none confirmable from the poster alone): (a) the F1 = 1 reference may correspond to an effective bioavailability lower than the steady-state F1 values reported for other strata; (b) the Table 3 NCA may have used the sparse-sampling visit schedule rather than the dense model-predicted profiles; (c) a transcription / scaling difference between the model’s internal units and the reported NCA units. Users requiring quantitative agreement with the source-paper NCA should treat the model as a structurally consistent population PK template and re-anchor the bioavailability (or the dose amount) to the observed exposure.